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Question: If the line y = 2x + l be a tangent to the hyperbola 36x<sup>2</sup> – 25y<sup>2</sup> = 3600, then...

If the line y = 2x + l be a tangent to the hyperbola

36x2 – 25y2 = 3600, then l =

A

16

B

–16

C

± 16

D

None of these

Answer

± 16

Explanation

Solution

line y = 2x + l

Hyperbola 36x2 – 25y2 = 3600

Žx2100\frac{x^{2}}{100}y2144\frac{y^{2}}{144} = 1

Now C = ±a2m2b2\sqrt{a^{2}m^{2} - b^{2}}

l = ±100(4)144\sqrt{100(4) - 144} = 256\sqrt{256}

Ž l = ± 16